The invention relates to optical devices based on parametric processes in non-linear waveguides.
In a non-linear process involving multiple interacting fields of different frequencies, the phase velocities at the different frequencies will usually differ. As a result there will be no significant net energy transfer between the different interacting fields unless measures are taken to provide overall phase matching. Phase matching requires that the relative phase mismatch between the interacting fields is zero over the length of the optical path. Phase matching can be achieved in several ways, of which so-called quasi phase matching (QPM) is one widely used technique [1].
QPM is based on the idea of providing a periodic modulation of the non-linear susceptibility "khgr" along the optical path of a non-linear material, with the periodic modulation having a period xcex1 matched to the length over which two interacting fields develop a relative phase mismatch of half a period, xcfx80. In fact, QPM does not address the phase mismatch locally, but provides overall compensation between regions of differing non-linearity, so that efficient net energy transfer from a pumping wave to a signal wave can take place.
For a second order non-linear (SON) parametric down conversion (PDC) process of the kind xcfx89p=xcfx89s+xcfx89i where xcfx89p. xcfx89i and xcfx89i are the pump, signal and idler frequencies, respectively, the phase matching (PM) condition can be expressed as:
xcex94xcex2=xcex2(xcfx89p)xe2x88x92(xcfx89s)xe2x88x92xcex2(xcfx89i)=0 
where xcex2(xcfx89p) xcex2(xcfx89s) and xcex2(xcfx89i) are the propagation constants of the pump, signal and idler waves, respectively.
Other expressions hold for different non-linear processes, such as third harmonic generation, four-wave mixing etc. For example, for second harmonic generation (SHG) in which a pump beam is used to generate a frequency-doubled signal, the PM condition can be expressed as xcex94xcex2=xcex2(2xcfx89)xe2x88x922xcex2(xcfx89)0.
It is mentioned that the SHG and PDC processes may be considered to be the reverse of each other. In the low conversion regime, in which the undepleted pump approximation holds, SH efficiency and the parametric gain assume similar expressions [3, 12]. Moreover, the bandwidth BW for SHG corresponds to the bandwidth BW for PDC, when they are read in terms of SH wavelength and pump wavelength respectively. However, the bandwidth BW for the PDC process for signal and idler wavelengths (for a fixed pump wavelength) is much broader, in particular at degeneracy [3, 12]. In the following, bandwidth is discussed in terms of SHG, although the findings can be extended to the pump bandwidth in a PDC process.
Returning to the specific example of the SON-PDC process, quasi phase matching includes an additional grating contribution term m(27c/xcex9) which arises from the periodic modulation for the m-th order harmonic, assuming a square-wave modulation of the non-linear properties. The QPM condition is then:
xcex94xcex2=(xcfx89p)xe2x88x92xcex2(xcfx89s)xe2x88x92xcex2(xcfx89i)xe2x88x92m(2xcfx80/xcex9)=0 
It is also known that the efficiency xcex7 of a parametric process in the low conversion efficiency regime is given by the expression:
xcex7xe2x88x9dL2sinc2(xcex94xcex2L/2) 
where L is the interaction length. Thus, efficiency can be improved by increasing the interaction length L (where xcex94xcex2xcx9c0) or reducing xcex94xcex2, i.e. by better satisfying the QPM condition. For example, it will be possible to determine for a given non-linear material the variation of efficiency of a non-linear process as a function of signal and/or pump frequency, efficiency being maximized for the set of wavelengths which satisfy the QPM condition.
The usable bandwidth for a non-linear process can be defined in terms of a threshold of sinc2 (xcex94xcex2L/2), such as:
sinc2(xcex94xcex2L/2)xe2x89xa7xc2xd
which can be rewritten as:
xcex94xcex2xe2x89xa60.886xcfx80/L 
from which it is apparent that, while a long interaction length L improves efficiency, it narrows the bandwidth. The only way of improving efficiency without sacrificing bandwidth is thus by improving the phase matching, i.e. by reducing xcex94xcex2.
The design of a waveguide structure for parametric processes has to consider several parameters, including efficiency, bandwidth, and single mode operation. In the low conversion regime, and assuming a uniform non-linearity across the beam profile, the SHG efficiency (or parametric gain in PDC) is of the form                     η        ∝                                            L              2                                      A              ovl                                ⁢          sin          ⁢                      xe2x80x83                    ⁢                                    c              2                        ⁡                          (                                                Δβ                  ⁢                                      xe2x80x83                                    ⁢                  L                                2                            )                                                          (        1        )            
where Aovl is the effective area which takes account of the overlap of the interacting waves: Aovl=1/Iovl2 where the overlap intensity Iovl=|∫ESH*EF2dA | with ESH and EF the normalised second harmonic (SH) and fundamental transverse profile respectively-defined so that ∫|ESH|2dA=∫|EF|2dA=1. The other parameters of the expression have already been defined. The effect of the factors xcex94xcex2 and L on efficiency xcex7 has already been discussed. From this equation it is however also apparent that efficiency xcex7 can be increased by reduction of the effective overlap area Aovl in absolute units of area (and increase of the degree of overlap)
Having now described the basic design considerations for designing devices based on non-linear effects, the prior art is reviewed.
Efficient QPM-SHG and PDC have been demonstrated in periodically poled ferroelectrics waveguides [2a, 2b] and glass fibers [3, 12]. Through the use of considerable interaction lengths L, good efficiency has been achieved in SHG devices, at the cost of limited bandwidth BW and lack of single mode operation at all wavelengths.
These prior art periodically poled ferroelectrics waveguides and glass fibers thus cannot deliver the large bandwidth that is important to ensure stable operation of SHG devices (for example temperature stability when high power is involved) or for SHG devices operating in the pulsed regime where one requires that interaction occurs for all the spectral components of the pulse.
Moreover, in the case of PDC (or difference frequency generation) a broad pump wavelength bandwidth is crucial for certain applications, for example in the routing of a multi-channel WDM system when one wants to have the possibility to switch from any channel into any other channel using difference frequency generation. The fact that typically one has large signal and idler bandwidths and narrow pump bandwidths means that routing around the degenerate point is possible, but not from one channel close to this point to another far from it (this would imply the use of other pump wavelengths). Basically, the device would function as an efficient spectral inverter [4].
To enhance the product of bandwidth and interaction length, BWxe2x80xa2L, it has been proposed to use aperiodic QPM structures [5]. The resulting efficiency is however small compared to that achievable for the same device length with a periodic QPM structure due to a reduction of the effective interaction length L.
As far as single mode operation in QPM-PDC (and difference frequency generation) devices is concerned, it has been proposed that complex waveguide structures [6] can be used to launch efficiently the pump at short wavelength into a waveguide which is single mode for the idler and the signal frequencies. For example, the signal and idler may be generated at around 1.5 xcexcm from a 0.75 xcexcm pump in a waveguide with a first cut-off wavelength at 1.3 xcexcm. The pump needs to be launched into the mode that satisfies the QPM condition at both the fundamental signal mode frequency and the idler mode frequency. Usually, the mode at the pump frequency also has to be the fundamental mode for efficient operation, i.e. good coupling efficiency and mode overlap.
Another proposed solution to provide single mode operation is to use cascading of the SON. A pump (with frequency close to that of signal and idler) is frequency doubled and subsequently down converted in the same waveguide structure [4]. This method has the drawback that longer waveguides are needed to achieve similar efficiency with respect to the former situation where a pump at twice the frequency of the signal and idler is launched into the waveguide.
In summary, with the prior art QPM device designs, there is generally a trade-off between the important design parameters of efficiency, bandwidth and the requirement of single mode operation.
It is therefore an aim of the invention to relax these design constraints so that QPM devices can be made with an improved combination of efficiency and bandwidth together with single mode operation.
According to one aspect of the invention there is provided a device based on a parametric process involving first and second frequencies xcfx891 and xcfx892 that differ, the device comprising an optical fiber comprising a core and a cladding, the optical fiber being poled with a non-linearity profile having a period that satisfies a quasi phase matching (QPM) condition including the first and second frequencies, wherein the cladding of the optical fiber comprises a hole structure for providing waveguiding confinement of at least one optical mode in the core.
Through the use of a poled holey fiber of suitable hole structure, it is possible to increase the SH efficiency xcex7 as defined in Equation (1) in comparison with poled conventional (non-holey) fiber. One factor contributing to the high efficiency is the increase in the bandwidth-length product, which can be order of magnitude greater than for conventional fiber. Another factor contributing to the high efficiency is the ability of a holey fiber to provide a low fundamental mode area and a low SH mode area combined with good overlap between the fundamental mode and the SH mode. It is the combination of properties relating to mode area and SH bandwidth, each of which can be individually tailored in a holey fiber structure, that together allow a high efficiency xcex7 to be achieved.
Another important factor is the ability in holey fiber structures to control dispersion properties. As well as allowing control of the linear dispersion, the microstructuring with holes can provide a low value of the group velocity mismatch GVM=(dxcex2/dxcfx89)xcfx891xe2x88x92(dxcex2/dxcfx89)xcfx892 and higher order dispersion terms. A low value of GVM is important in determining phase matching properties of processes that involve significantly different wavelengths.
Specifically, in the case of SHG, the phase mismatch can be written as follows:
xcex94xcex2=xcex2(2xcfx89)xe2x88x922xcex2(xcfx89)=2[(dxcex2/dxcfx89)2 xcfx89oxe2x88x92(dxcex2/dxcfx89)xcfx89o][xcfx89xe2x88x92xcfx890]+[2(d2xcex2/dxcfx892)2xcfx89oxe2x88x92(d2xcex2/dxcfx892)xcfx89][xcfx89xe2x88x92xcfx890]2= . . . xe2x80x83xe2x80x83(2) 
where xcfx890 is the PM or QPM fundamental frequency. From this expression it can be understood that large bandwidths are obtainable. This is achieved in some solutions by minimizing the first order term of the expansion so that GVM=(dxcex2/dxcfx89)2xcfx89oxe2x88x92(dxcex2/dxcfx89)xcfx89oxe2x86x920, and similarly minimizing the higher order terms. In other solutions, the different order terms together cancel or offset each other.
Further details of GVM and its role in determining phase matching properties are discussed in the context of traditional optical fibers in reference [10]. With conventional optical fibers, it was shown that GVM tends to zero for fundamental wavelengths xcx9c1.8 xcexcm which is too long a wavelength to be of interest for general telecommunications applications around wavelengths of 1.3 or 1.55 xcexcm. Using dispersion shifted and non-zero dispersion fibers it may be possible to shift the GVM zero point to shorter wavelengths, but only perhaps to 1.6-1.7 xcexcm. By contrast, as discussed in the following, with the invention it is possible to shift the GVM zero point below 1.6 xcexcm while simultaneously ensuring that higher order dispersion terms in Equation (2) cancel each other, at least partially.
Through the use of a poled holey fiber of suitable hole structure, it is also possible to overcome the difficulties in achieving single mode operation in the prior art straightforwardly, since the hole structure can be designed to be single-mode for the first and second frequencies xcfx891 and xcfx892 of the parametric process, even when the values are widely differing. In fact, it is possible to make the poled holey fiber single mode for all interacting wavelengths of the parametric process, so-called endlessly single-moded fiber [7].
Here it is noted that single mode operation at both the first frequency xcfx891 and the second frequency xcfx892 of the parametric process is highly desirable for simple parametric processes in which the pump interacts directly with the signal, e.g. xcexS=1505 xcexcnm, xcexi=1495 nm and xcexpxcx9c750 nm (where xcex is wavelength) for a process xcfx89pxe2x88x92xcfx89sxe2x86x92xcfx89i. However, for cascaded processes, efficient operation can be provided without single mode operation at all relevant frequencies, e.g. xcexs=1505 nm, xcexi=1495 nm and xcexpxcx9c1500 nm for a cascaded process xcfx89p+xcfx89pxe2x86x922xcfx89p followed by 2xcfx89pxe2x88x92xcfx89sxe2x86x92xcfx89i. In this example, since the conversion process xcfx89p+xcfx89pxe2x86x922xcfx89p takes place in the fiber, single mode operation is not needed at 2xcfx89p, but only at the closely interspaced frequencies xcfx89p, xcfx89s and xcfx89i.
A variety of other choices of the fundamental wavelength are possible. In particular, the fact that holey fiber can be made of a single material allows the full transmission window of the material concerned to be used for frequency conversion. For example, in a pure silica holey fiber visible light can be frequency doubled into the ultraviolet. One example of a suitable optical glass for making poled holey fiber is the silica glass Herasil (trade name).
Holey fibers are discussed in the prior art [7]. In particular, it is known in the prior art that holey fibers can be designed with small effective areas to provide high efficiency third-order nonlinear processes, e.g. four-wave mixing (FWM) [8]. In fact for nearly-degenerate operation the BW for a FWM process is inversely proportional, in first-order approximation, to the value of d2/dxcfx892 which can be kept nearly zero over a wide range of wavelength using particular designs [9]. However, this work does not relate to broadband parametric processes involving disparate frequencies.
Further studies applying the theory of reference [9] have been carried out which indicate that the desired combination of single mode operation, broad bandwidth and good efficiency is achievable with a wide variety of hole structures. It is possible to calculate the relevant device parameters for any proposed hole structure using the theory of reference [9]. In that way, a suitable hole structure can be decided upon prior to fabrication.
According to another aspect of the invention there is provided a method of fabricating a device based on a parametric process involving first and second frequencies xcfx891 and xcfx892 that differ, the method comprising: providing an optical fiber having a hole structure; and poling the optical fiber to generate a non-linearity profile having a period that satisfies a quasi phase matching (QPM) condition including the first and second frequencies.
The poling is preferably carried out using a so-called optical poling method, as described in reference [11], the contents of which are incorporated herein by reference. Namely, the poling preferably comprises: thermal poling of the optical fiber to generate a non-linearity therealong; placing a mask adjacent to the optical fiber; and exposing the optical fiber with UV light through the mask to selectively erase the non-linearity along the waveguide structure thereby to generate the non-linearity profile having the period that satisfies the QPM condition. The mask may be an amplitude mask or a phase mask.
In an embodiment, the thermal poling comprises maintaining the optical fiber at an elevated temperature (typically a few hundred degrees Celsius) while applying an electric field across the hole structure. The first and second electrodes are arranged to straddle the hole structure.
As described further below, it is possible to fabricate electrodes integral to the optical fiber close to the optically active part of the fiber.
A particular advantage of the optical poling method, as opposed to more conventional thermal poling, is that no electrode structuring is required. Continuous electrodes can be used. This is important, since continuous electrodes can be conveniently arranged embedded in the holey fiber structure. The electrodes may be inserted after drawing the holey fiber, or may be formed integrally with the holey fiber during the fiber drawing process. In this way, it is possible to place the electrodes close together straddling the optically active area of the waveguide where the mode is confined so that large electric fields can be generated in this region to provide good poling.
By contrast, it would be less attractive to form patterned or structured electrodes onto the holey fiber, as would be required for thermal poling. Nevertheless, alternative embodiments of the invention may use thermal poling. For example, the thermal poling may involve deposition of a patterned electrode on the outer surface of the fiber, as described in reference [12]. Alternatively, the outer surface of the fiber may be structured as described in reference [13], the contents of which are incorporated herein by reference.